Question 39
$n=10000$ contestants take part in a mathematics competition.
At the final party, in succession, the first one takes $1/n$ of the cake, the second takes $2/n$ of the remaining cake, the third takes $3/n$ of the cake remaining after the first and the second have served themselves, and so on until the last one, who takes all the remaining cake.
Determine which contestant takes the largest piece of cake.
At the final party, in succession, the first one takes $1/n$ of the cake, the second takes $2/n$ of the remaining cake, the third takes $3/n$ of the cake remaining after the first and the second have served themselves, and so on until the last one, who takes all the remaining cake.
Determine which contestant takes the largest piece of cake.